US8114489B2 - Composite material having low electromagnetic reflection and refraction - Google Patents
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- US8114489B2 US8114489B2 US10/153,502 US15350202A US8114489B2 US 8114489 B2 US8114489 B2 US 8114489B2 US 15350202 A US15350202 A US 15350202A US 8114489 B2 US8114489 B2 US 8114489B2
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Definitions
- the present invention is related to materials having low electromagnetic reflection and refraction.
- the invention generally concerns materials provided to control electromagnetic reflection and refraction.
- electromagnetic radiation The behavior of electromagnetic radiation is altered when it interacts with charged particles. Whether these charged particles are free, as in plasmas, nearly free, as in conducting media, or restricted, as in insulating or semi conducting media—the interaction between an electromagnetic field and charged particles will result in a change in one or more of the properties of the electromagnetic radiation. Because of this interaction, media and devices can be produced that generate, detect, amplify, transmit, reflect, steer, or otherwise control electromagnetic radiation for specific purposes.
- the behavior of electromagnetic radiation interacting with a material can be predicted by knowledge of the material's electromagnetic materials parameters ⁇ and ⁇ where ⁇ is the electric permittivity of the medium, and ⁇ is the magnetic permeability of the medium. These parameters represent a macroscopic response averaged over the medium, the actual local response being more complicated to describe and generally not necessary to describe the electromagnetic behavior.
- Reflection and transmission at the interface between two media are governed by the index of refraction ⁇ and impedance z of each medium.
- the index ⁇ and the impedance z are directly related to the reflection and transmission properties of a slab of material, and hence are the observable quantities that correspond directly to the electromagnetic performance of materials.
- the relative index of refraction and the relative electromagnetic impedance z of air are often taken to be equal to unity.
- a material that is electromagnetically “transparent” will have both its index of refraction and impedance numerically close to that of the surrounding medium.
- Such a material is valuable for many applications.
- airplanes may have a collision detection radar system mounted near their “nose.” This system operates inside a composite dome known as a radome that has a shape optimized for aerodynamic properties.
- the radar system must compensate for the lensing effects of the shaped radome composite material, which typically has a relative index of refraction that is significantly greater than unity. Such compensation requires effort and expense, and is subject to error.
- structural materials may be used to embed a sensor such as an array of antennas in a wireless communications device. Reflection and refraction effects in these structural materials are likewise undesirable.
- material requirements irrespective of their electromagnetic reflection and refraction properties, include physical properties such as strength, ductility, and resistance to heat, cold, and moisture. The prior art has had limited success in satisfying these needs.
- Materials and methods for generally minimizing electromagnetic reflection and maximizing transparency have been proposed. For example, materials have been proposed that have a high absorption of incident radiation at microwave and other frequencies. In addition to preventing transmission of radiation, the strong absorbance of these materials often leads to a substantial reflected component. As a result, use of these materials is usually accompanied by irregular material shapes and surface angles required to direct the reflected component in a desired direction. The required irregular surface angles and shapes significantly limit the utility of such materials and methods.
- the prior art has employed particular naturally occurring media that may be found in nature or that can be formed by known chemical synthesis and that may have a low level of electromagnetic reflection over a particular frequency range. Use of such media is disadvantageously limited to these particular frequency ranges. Also, it is difficult to find media with significant permeability at RF and higher frequencies. These media may also be structurally unsuitable for many applications.
- An example of a prior art artificial dielectric material is the “rodded” medium, used as an analogue medium to study propagation of electromagnetic waves through the ionosphere [See, e.g., R. N. Bracewell, “Analogues of an Ionized Medium”, Wireless Engineer, 31:320-6, December 1954, herein incorporated by reference].
- An artificial medium based on conducting wires or posts has a dielectric function identical to that describing a dilute, collisionless neutral plasma. Accordingly, as used herein a medium based on conducting wires will be referred to as a “plasmonic” medium. More recently, artificial plasmonic media have been proposed using, for example, a periodic arrangement of very thin conducting wires. See, e.g., J. B.
- the present invention is directed to a composite material comprising a host dielectric medium having an index of refraction greater than 1, and an artificial plasmon medium embedded in the host medium.
- the artificial plasmon medium has a dielectric function of less than one so that the permittivity of the composite material is substantially equal to that of the surrounding medium for incident electromagnetic radiation of a desired frequency.
- Composite media of the invention thus can be of utility as materials that are highly transparent and exhibit minimal reflectance or refraction for electromagnetic waves in a desired frequency range. Also, composite media embodiments of the present invention can be “tuned” for achieving transparency and/or minimal reflection and refraction for electromagnetic waves in the desired frequency range through selection of particular conductor/host materials, conductor/host sizing and/or spacing, and conductor/host geometric configuration. Further, composite media of the present invention allow for achieving these desired electromagnetic properties (e.g., transparency and low reflection) while providing advantageous structural and mechanical properties, with the result that embodiments of the present invention will be well suited for applications such as radomes, antennas, and the like.
- desired electromagnetic properties e.g., transparency and low reflection
- FIG. 1( a ) is a graphical representation of the relationship between a matrix dielectric constant and a normalized frequency
- FIG. 1( b ) is a graphical representation of the relationship between the matrix dielectric constant and a bandwith;
- FIG. 1( c ) is a top plan cross section of a preferred embodiment of a composite material of the invention
- FIG. 2 is a side elevational cross section of the embodiment of FIG. 1 taken along the line 2 - 2 ;
- FIG. 3 is a top plan cross section of an additional preferred embodiment of a composite material of the invention.
- FIG. 4 is a schematic perspective of the embodiment of FIG. 3 ;
- FIG. 5 is a top plan cross section of an additional preferred embodiment of a composite material of the invention.
- FIG. 6 is a perspective schematic representation of the embodiment of FIG. 5 ;
- FIG. 7 is a perspective schematic representation of an additional preferred embodiment of a composite material of the invention.
- FIG. 8 is a top plan schematic representation of the embodiment of FIG. 7 ;
- FIGS. 9( a )-( c ) illustrate some alternative conductors of the invention.
- FIG. 10 is a side elevational view of a portion of an additional preferred embodiment of the invention.
- FIG. 11 is a top plan cross-section view of a portion of the embodiment of FIG. 10 ;
- FIGS. 12( a ) and ( b ) are plots showing computer simulation based electrical properties of the embodiment of FIG. 11 ;
- FIG. 13 is a perspective view of a preferred radome embodiment of the invention.
- FIG. 14 is a bottom plan view of the radome embodiment of FIG. 13 .
- Maxwell's equations In order to describe the presence of a material, Maxwell's equations must be solved in the presence of the material.
- the local electromagnetic response of a material the exact electric and magnetic field distributions that occur near the atoms or elements that compose the material—will in general be very complicated.
- the local fields are typically averaged to obtain a set of Maxwell's equations that includes the material properties in two parameters: ⁇ and ⁇ .
- Drude medium which in certain limits describes such systems as conductors and dilute plasmas.
- f is the electromagnetic excitation frequency
- f p is the plasma frequency
- v is a damping factor.
- the plasma frequency may be thought of as a limit on wave propagation through a medium: waves propagate when the frequency is greater than the plasma frequency, and waves do not propagate (e.g., are reflected) when the frequency is less than the plasma frequency.
- Simple conducting systems such as plasmas have a dispersive dielectric response.
- the degree to which an artificial medium obeys EQTN. A must often be determined empirically and depends on the construction materials and on the geometric properties that determine f p relative to the inter-element spacing of the metal scattering elements.
- the plasma frequency f p usually occurs in the optical or ultraviolet bands.
- the Pendry reference that has been incorporated herein by reference teaches a thin wire media—in which the wire diameters are significantly smaller than the skin depth of the metal—can be engineered with a plasma frequency in the microwave regime, below the point at which diffraction due to the finite wire spacing occurs. By restricting the currents to flow in thin wires, the effective charge density is reduced, thereby lowering the plasma frequency. Also, the inductance associated with the wires acts as an effective mass that is larger than that of the electrons, further reducing the plasma frequency. By incorporating these effects, the Pendry reference provides the following prediction for the plasma frequency of a thin wire medium:
- f p 2 1 2 ⁇ ⁇ ⁇ ( c 0 2 / d 2 ln ⁇ ( d r ) - 1 2 ⁇ ( 1 + ln ⁇ ⁇ ⁇ ) )
- c 0 is the speed of light in a vacuum
- d is the thin wire lattice spacing
- r is the wire diameter.
- the length of the wires is assumed to be infinite and, in practice, preferably the wire length should be much larger than the wire spacing, which in turn should be much larger than the radius.
- the Pendry reference suggests a wire radius of approximately one micron for a lattice spacing of 1 cm—resulting in a ratio, d/r, on the order of or greater than 10 5 .
- the charge mass and density that generally occurs in the expression for the f p are replaced by the parameters (e.g., d and r) of the wire medium.
- the interpretation of the origin of the “plasma” frequency for a composite structure is not essential to this invention, only that the frequency-dependent permittivity have the form as above, with the plasma (or cutoff) frequency occurring in the microwave range or other desired ranges.
- any conducting element that has an inductance can also be utilized as the repeated element that forms a plasmonic medium.
- increased inductance is primarily achieved by making the wires very thin; However, the inductance can also be increased by other means, such as arranging inductive loops within the medium, or even the inclusion of actual inductive elements within the circuit.
- Thicker loop-wire media can be comprised, for example, of wire coils or wire lengths having periodic loops.
- An embodiment of the present invention is directed to a composite, or hybrid, material comprised of a host dielectric with an artificial plasmon medium embedded therein, whereby the composite material has an index of refraction and impedance both substantially equal to that of the surrounding medium.
- index of refraction and impedance of the medium are both measured relative to the surrounding medium, and accordingly the term “relative” as used herein in describing terms such as “index” and “impedance” is intended to refer to a comparison to the surrounding medium.
- An invention embodiment may be considered an artificial plasmon medium.
- Behavior of embodiments of the present invention is modeled on the assumption that the host dielectric has a uniform dielectric constant or function (it is noted that as used herein the terms dielectric constant and dielectric function are intended to be interchangeable). However, an effective dielectric function of the host medium can be substituted for the uniform constant and the properties in the frequency range of interest will be substantially unchanged.
- the conductivity of the conducting elements of the composite embodiments of the present invention approaches infinity, but any good metal conductor such as copper or silver provides a close behavioral agreement to ideal simulations.
- a conductor of the present invention may be varied in spacing and/or geometry to control the plasma frequency ⁇ p ,and thereby “tune” the composite of the invention.
- the dielectric function of the composite of course changes upon addition of the dielectric.
- the dipolar response term ⁇ 0 is substantially equal to the effective dielectric constant of the polymer composite matrix in the absence of the integrated artificial plasmon medium when that medium closely obeys EQTN. A and also occupies a negligible volume fraction of the composite.
- FIGS. 1( a ) and 1 ( b ) illustrate the dependence of f 0 and f on the matrix dielectric function.
- FIG. 1 ( a ) shows the turn-on frequency f 0 (dashed line) and match frequency f 1 (solid line) as a function of the matrix dielectric constant ⁇ 0 where the normalized frequency is in units of the plasma frequency f p
- FIGS. 1( c ) and 2 show a top plan cross section and a side elevational cross section, respectively, of a portion of an embodiment of a composite material 10 of the present invention.
- the composite material 10 comprises a dielectric host 12 and a conductor 14 embedded therein.
- dielectric as used herein in reference to a material is intended to broadly refer to materials that have a relative dielectric constant greater than 1, where the relative dielectric constant is expressed as the ratio of the material permittivity ⁇ to free space permittivity ⁇ 0 (8.85 ⁇ 10 ⁇ 12 F/m).
- dielectric materials may be thought of as materials that are poor electrical conductors but that are efficient supporters of electrostatic fields. In practice most dielectric materials, but not all, are solid. Examples of dielectric materials useful for practice of embodiments of the current invention include, but are not limited to, porcelain such as ceramics, mica, glass, and plastics such as thermoplastics, polymers, resins, and the like.
- conductor as used herein is intended to broadly refer to materials that provide a useful means for conducting current. By way of example, many metals are known to provide relatively low electrical resistance with the result that they may be considered conductors. Preferred conductors for the practice of embodiments of the invention include aluminum, copper, gold, and silver.
- the preferred conductor 14 comprises a plurality of portions that are generally elongated and parallel to one another, with a space between portions of distance d.
- d is less than the size of a wavelength of the incident electromagnetic waves. Spacing by distances d of this order allow the composite material of the invention to be modeled as a continuous medium for determination of permittivity ⁇ .
- the preferred conductors 14 have a generally cylindrical shape.
- a most preferred conductor 14 comprises thin copper wires. These conductors offer the advantages of being readily commercially available at a low cost, and of being relatively easy to work with. Also, matrices of thin wiring have been shown to be useful for comprising an artificial plasmon medium, as discussed by Pendry et al., “Extremely Low Frequency Plasmons in Metallic Mesostructures,” Physical Review Letters, 76(25):4773-6, 1996; incorporated by reference herein.
- FIG. 3 is a top plan cross section of another composite material embodiment 20 of the present invention.
- the composite material 20 comprises a dielectric host 22 and a conductor that has been configured as a plurality of portions 24 .
- the conductor portions 24 of the embodiment 20 are preferably elongated cylindrical shapes, with lengths of copper wire most preferred.
- the conductor portions 24 are preferably separated from one another by distances d 1 and d 2 as illustrated with each of d 1 and d 2 being less than the size of a wavelength of an electromagnetic wave of interest. Distances d 1 and d 2 may be, but are not required to be, substantially equal.
- the conductor portions 24 are thereby regularly spaced from one another, with the intent that the term “regularly spaced” as used herein broadly refer to a condition of being consistently spaced from one another. It is also noted that the term “regularly spacing” as used herein does not necessarily require that spacing be equal along all axis of orientation (e.g., d 1 and d 2 are not necessarily equal). Finally, it is noted that FIG. 3 (as well as all other FIGS.) have not been drawn to any particular scale, and that for instance the diameter of the conductors 24 may be greatly exaggerated in comparison to d 1 and/or d 2 .
- each planar layer 26 represents a plurality of parallel conductors 24
- the dielectric host 22 is illustrated as a transparent dashed line “box”.
- the embodiment 20 may also be thought of as having each plane of its conductors 24 in a single “dimension.” That is, the conductors 24 in each plane generally lie along a single axis of orientation (e.g., the x-axis).
- FIGS. 5 and 6 illustrates the conductors 52 oriented along two axes and embedded in a dielectric host 54 .
- the conductors 52 in the composite material embodiment 50 may be thought to generally extend along both the x-axis and the y-axis. This is illustrated schematically in FIG. 6 , with the conductors 52 represented as lines, and the dielectric host 54 represented as a dashed line box.
- Such a configuration thereby can also be considered to have a plurality of first conductors 52 organized into substantially planar rows, and a plurality of second conductors 52 organized into substantially planar columns.
- planar columns are preferably separated from one another by a distance less than a wavelength of electromagnetic wave of interest, with the planar rows likewise preferably spaced.
- inventions may additionally comprise conductors oriented along additional axes.
- a composite material 100 is represented schematically in the perspective view of FIG. 7 and the top plan view of FIG. 8 .
- a plurality of conductors 102 represented as lines may be oriented along the x, y and z axis to result in a “three dimensional” configuration.
- conductor orientations are also possible within the present invention.
- conductors of embodiments of the present invention may comprise configurations other than substantially straight portions as shown in the embodiments 10 , 20 , and 50 . Indeed, depending on a particular application it may be desirable to “tune” the composite material by altering the electrical properties of the conductor. By way of example, the diameter, geometry, and/or spacing of the conductor could be altered. With reference to FIGS. 9( a )-( c ) by way of example, alternate conductor shapes are illustrated.
- FIG. 9( a ) shows conductors 150 with a plurality of loops 152 .
- the loops 152 are preferably of substantially uniform diameter, and are preferably substantially regularly spaced along the length of the conductors 150 .
- a substantially uniform distance preferably separates each loop 152 along a length of a conductor 150 .
- the loops 152 comprise inductive elements, and thereby serve to increase the impedance of the conductors 150 . Varying the diameter and number of the loops 152 will of course alter the electrical properties of the conductors 150 , and may thereby be used to further “tune” a resulting composite material so that the composite refractive index and/or reflection coefficient is substantially equal to 1.
- FIG. 9( b ) shows conductors 153 in the form of spring-like coils.
- the conductors 150 or 153 may be used in combination with a dielectric host to comprise a composite material of the invention.
- the conductors 150 or 154 could be used in any of the embodiments 10 , 20 , 50 or 100 of FIGS. 1 ( c )- 8 .
- FIG. 9( c ) shows an additional alternate conductor 155 embedded in a host dielectric 157 .
- the conductor 155 is characterized in that each conductor 155 has a number of individual linked portions that are substantially straight, are at right angles to one another, with each of the portions lying along one of the x, y or z axes.
- non-cylindrical geometries comprising substantially square, rectangular, or eleptical cross sections may be of use.
- FIG. 10 is a side elevational view of a portion of an additional embodiment 200 of the invention comprising a loop-wire artificial plasmon composite material.
- the embodiment 200 comprises a plurality of conductors 202 that may be considered to have the geometry of the conductors 150 or 154 of FIG. 9( a ) or ( b ). That is, the conductors 202 generally may comprise a plurality of connected loops, or may comprise coils.
- the conductors 202 are wrapped around a dielectric host, which is in the form of a plurality of elongated members 204 that may comprise by way of example nylon rods.
- the nylon rods are preferably substantially parallel to one another, and are preferably separated from one another by a substantially equal distance.
- FIG. 11 is a top plan cross section of a portion of the embodiment 200 , illustrating the conductor 202 surrounding the dielectric nylon rod host 204 .
- FIGS. 12( a ) and ( b ) illustrate the result of computer simulations run on the composite material 200 , using thin copper wire as the conductor having vertical spacing between loops of about 8 mm, horizontal spacing between rods of about 8 mm, and using 6-32 nylon rods.
- FIGS. 12( a ) and ( b ) show a predicted matching condition close to 8 GHz.
- One advantage of embodiments of the composite material of the present invention is that the composites can achieve mechanical strength and may be desirably conformed for particular applications. Indeed, those knowledgeable in the art will appreciated that using a preferred dielectric host such as a polymer and a preferred conductor such as thin copper wire, composite materials of the invention will lend themselves well to being readily configured to a multiplicity of applications.
- a composite material of the invention may have utility as an electromagnetically transparent “window” for covering electronics.
- Examples include, but are not limited to, mechanically protective but electromagnetically transparent electronics housings and cabinets, antennae for communications devices such as cellular phones and transmission centers, building materials for structures used for communications such as satellite stations, “stealth” materials for military applications including airplanes, ships, submarines, land vehicles, individual armor; and the like.
- FIGS. 13-14 A particular example is shown in FIGS. 13-14 , where a composite material 250 of the invention has been configured in the general shape of a “dome” for use as a radome for covering radar equipment.
- the perspective view of FIG. 13 shows the general “inverted bowl” shape of the radome 250 , with radar or other electronics equipment able to be covered by the radome 250 .
- the plan view of FIG. 14 illustrates the general circular circumference of the radome 250 .
- the radome 250 is constructed of a composite material of the invention, which may comprise by way of example plastic or glass having an embedded thin wire conductor matrix therein.
Abstract
Description
η=[(∈μ)/(∈0μ0)]1/2
z=(μ/∈)1/2/(μ0/∈0)1/2
where the
v=λf
The angular frequency ω is related to the frequency by a constant:
ω=2πf
In dimensionless quantities, then, ratios of frequencies can be used interchangeably:
(f 1 /f 2)=(ω1/ω2)
∈(f)/∈0=1−f p 2 /f(f+iv) EQTN. A
where f is the electromagnetic excitation frequency, fp is the plasma frequency and v is a damping factor. In general, the plasma frequency may be thought of as a limit on wave propagation through a medium: waves propagate when the frequency is greater than the plasma frequency, and waves do not propagate (e.g., are reflected) when the frequency is less than the plasma frequency. Simple conducting systems (such as plasmas) have a dispersive dielectric response. The degree to which an artificial medium obeys EQTN. A must often be determined empirically and depends on the construction materials and on the geometric properties that determine fp relative to the inter-element spacing of the metal scattering elements.
ωp =[n eff e 2/∈0 m eff]1/2
and
f p=ωp/2π
where neff is the charge carrier density and meff is an effective carrier mass. For the carrier densities associated with typical conductors, the plasma frequency fp usually occurs in the optical or ultraviolet bands.
where c0 is the speed of light in a vacuum, d is the thin wire lattice spacing, and r is the wire diameter. The length of the wires is assumed to be infinite and, in practice, preferably the wire length should be much larger than the wire spacing, which in turn should be much larger than the radius.
∈Ε/∈0=∈H/∈0−(ωp/ω)2
where ∈H is the permittivity of the host material and ω is the angular frequency of the electromagnetic radiation. Using the above relations, it may be derived that:
η=[∈H/∈0−(f p 2 /f 2)]1/2
η=(κ)1/2=[1−(f p 2 /f 2)]1/2
where κ=∈/∈0. The dielectric function of the composite of course changes upon addition of the dielectric. The presence of a dielectric matrix into which the plasmon medium is embedded will result in a polarization response that can be accounted for by introducing κ0 such that:
κ=κ0−(f p 2 /f 2)
where κ is the effective dielectric constant of an ideal plasmon/dielectric composite material. The dipolar response term κ0 is substantially equal to the effective dielectric constant of the polymer composite matrix in the absence of the integrated artificial plasmon medium when that medium closely obeys EQTN. A and also occupies a negligible volume fraction of the composite.
Claims (29)
∈eff=∈host−(f p/f)2
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